Hypertexts as educational systems: Pedagogical issues in teaching and learning mathematical problem solving
The aim of this paper is to present some research results on the relationship between new technologies (such as hypermedia systems) and learning; in particular we consider the case of learning how to solve calculus problems.
In the first part we try to highlight the conceptual bases of the research and its specific goals: the choice, or better the hypothesis, of a sequence of behaviors which express the mental states and which allow the reasoning about calculus problems or, more in general, about problem solving in mathematics. Then we realize the need of making the students aware of their learning processes through procedures that are proper to the metacognition. Finally we try to show how Hypercalculus, the hypermedia system for learning calculus we designed, and which is currently under test by a large number of students of the first year of a master degree in engineering at Politecnico di Torino, can be considered as an example of a computer aided learning tool.
Unable to display preview. Download preview PDF.
- J. R. Anderson, “The architecture of cognition”, Harvard University Press, Cambridge, MA, 1983.Google Scholar
- H. Freudenthal, “Revisiting mathematics education. China lectures”, Kluwer Academic Publishers, Dordrecht, 1991.Google Scholar
- C. Cornoldi, “Metacognizione e apprendimento”, Il Mulino, Bologna, 1995.Google Scholar
- A. H. Schoenfeld, “Metacognitive and epistemological issues in mathematical understanding”, in E. A. Silver (ed.), “Teaching and learning mathematical problem solving”, Erlbaum, Hillsdale, 1985.Google Scholar
- J. E. Davidson, R. Deuser, R. J. Sternberg, “The role of metacognition in problem solving”, in J. Metcalfe, R. Shimamura (eds.) “Metacognition: knowing about knowing”, MIT Press, Cambridge, MA, 1994.Google Scholar
- M. Dodman, “Tessere la realtà: ipertesti e ipertestualità”, in L'Educazione Matematica, XVI, IV, Vol. 2, 1995.Google Scholar
- A. Giannetti, P. L. Montessoro, A. R. Scarafiotti, “Hypermath: a calculus hypertext for distance learning”, in Proceedings of Teleteaching '93, Trondeim, Norway, August 20–25, 1993.Google Scholar
- A. R. Scarafiotti, A. Giannetti, “Hypermath: a hypertext for calculus teaching to learn in hypertextual form”, in Proceedings of the first Italian-Spanish Symposium in Mathematical Education, Modena, Italy, February 15–19, 1994.Google Scholar
- L. Farinetti, A. R. Scarafiotti, “Hypermedia in education: lots of theory and a little of practice”, in Proceedings of ED-MEDIA 95, World Conference on Educational Multimedia and Hypermedia, Graz, Austria, June 17–21, 1995.Google Scholar
- L. Farinetti, A. R. Scarafiotti, “Conoscenza e comunicazione in ipertesti per la didattica”, in Sistemi Intelligenti, VII, 2, 1995, pp. 291–303.Google Scholar
- A. R. Scarafiotti, A. Giannetti, F. Alloatti, “La produzione di senso nella gestione di problemi matematici: un sistema ipertestuale per imparare a risolvere esercizi di calculus”, in A. Gisolfi (ed.), Multimedia. Beni Culturali e Formazione, Elea Press, Salerno, 1994.Google Scholar
- B. S. Randhawa, J. E. Beamer, I. Lundberg, “Role of mathematics self-efficacy in the structural model of mathematics achievement”, in Journal of Educational Psychology, 85, 41/48, 1993.Google Scholar